Actually, the 'doubleback' feature hasn't been implemented in game yet, for technical reasons. It's still a feature they're working on, it's just not ready yet.

As for the 'back' of a card, that will look like whatever sleeve it is in. This backing is visible when the card is on top of your deck, and visible to your opponent when it is in your hand or tunneled underground. You can select the sleeve to use in the deckbuilder with the same menu you use to save and load decks, which will affect what sleeve you see on top of your deck.